Pyramidal versus Tetrahedral Elements in Finite Element Applications

A successful 3-D finite element code for Maxwell’s equations must include all four kinds of geometrical shapes: tetrahedrons, hexahedrons, triangular prisms, and square-based pyramids. For cells of the first three types, the scalar shape functions, the high-order curl-conforming and divergence-conforming vector bases are well known and available for a long time [1]. On the contrary, it has been much more difficult to derive higher-order functions and bases of the same kind for pyramidal cells, so much so that those accessible in the literature until recently are obtained with extremely complex ad hoc techniques [2].